Wheel loader trajectories between loading and unloading positions in a repetitive loading cycle are studied. A wheel loader model available in the literature is improved for better fuel estimation and optimal control problems are formulated and solved using it. The optimization results are analyzed in a side to side comparison with measurement data from a real world application. It is shown that the trajectory properties affect the operation productivity. However, efficient trajectories are not the only requirement for high productivity operation and all major power consuming sources such as vehicle dynamics, lifting and steering have to be included in the optimization for productivity analysis. The effect of operator steering capability is also analyzed showing that development of autonomous vehicles can be envisaged especially for repetitive cycles.

Nonlinear model predictive control (NMPC) has become increasingly important for today's control engineers during the last decade. In order to apply NMPC a nonlinear optimal control problem (NOCP) must be solved which in general needs high computational effort.State-of-the-art solution algorithms are based on multiple shooting or collocation algorithms, which are required to solve the underlying dynamic model formulation. This paper describes a general discretization scheme applied to the dynamic model description which can be further concretized to reproduce the multiple shooting or collocation approach. Furthermore, this approach can be refined to represent a total collocation method in order to solve the underlying NOCP much more efficiently. Further speedup of optimization has been achieved by parallelizing the calculation of model specific parts (e.g. constraints, Jacobians, etc.) and is presented in the coming sections.The corresponding discretized optimization problem has been solved by the interior optimizer Ipopt. The proposed parallelized algorithms have been tested on different applications. As industrial relevant application an optimal control of a Diesel-Electric power train has been investigated. The modeling and problem description has been done in Optimica and Modelica. The simulation has been performed using OpenModelica. Speedup curves for parallel execution are presented.

Optimal control of a wheel loader operating in the short loading cycle is studied in order to investigate the potentials for fuel consumption reduction while maintaining acceptable production rates. The wheel loader is modeled as a system with five states and three control inputs including torque converter nonlinearities. The torque converter is modeled with no lockup enabling power transmission in both directions. The geometry of the wheel loader boom and the demanded force in the lift cylinders during lifting are used to ensure that the in-cylinder pressure remains below component's limits. The lift-transport section of the short loading cycle is divided into four phases due to discontinuities in the gearbox ratios and fuel consumption is calculated in each phase. Time optimal and fuel optimal transients of the system and the power consumption in each and every component is presented showing the dominance of the torque converter losses compared to the other components especially in the time optimal solutions. It is shown that introducing path constraints on the maximum lifting speed of the bucket due to limitations in hydraulic pumping speed moves the diesel engine operation towards higher speeds in order to maintain the lifting speed. Trade-off between fuel optimal and time optimal transients is calculated which is found to be in agreement with the results of experimental studies.

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The importance of including turbocharger dynamics in diesel engine models are studied, especially when optimization techniques are to be used to derive the optimal controls. This is done for two applications of diesel engines where in the first application, a diesel engine in wheel loader powertrain interacts with other subsystems to perform a loading operation and engine speed is dictated by the wheel speed, while in the second application, the engine operates in a diesel-electric powertrain as a separate system and the engine speed remains a free variable. In both applications, mean value engine models of different complexities are used while the rest of system components are modeled with the aim of control study. Optimal control problems are formulated, solved, and results are analyzed for various engine loading scenarios in the two applications with and without turbocharger dynamics. It is shown that depending on the engine loading transients, fuel consumption and operation time can widely vary when the turbocharger dynamics are considered in the diesel engine model. Including these, have minor effects on fuel consumption and operation time at minimum fuel operations of the first application (≈ 0:1%) while the changes are considerable in the second application (up to 60%). In case of minimum time operations however, fuel consumption and operation time are highly affected in both applications implying that not considering turbocharger dynamics in the diesel engine models may lead to overestimation of the engine performance especially when the results are going to be used for control purposes.